I have the 28-300 and the 24-120 for my D800. In my case, the 24-120 produces much sharper pictures in every situation. That said, at the sizes I typically upload to Flickr, the difference is not noticeable. The 24-120 focuses faster.

I don't know if it's all 28-300's or just my copy, but it's freakishly sharp at 300mm. I have some test shots using a 300 f2.8 and the result (in the center) is almost the same. All focal lengths that are not 300mm are much less sharp.

It certainly sounds like you got a poor copy. Sadly these consumer lenses are hit or miss.